by Benjamin N. Grosof

Abstract:
Expressively rich non-monotonic reasoning is significantly more
computationally difficult, in the worst case, than monotonic reasoning
(over the same base language). An interesting direction of research,
therefore, is to find expressively restricted cases for which it is
relatively easy. In this paper (adapted and revised from parts of our
PhD thesis), we give a new such case: the class of what we call
sympathetically solitary default theories. For this class, we are
able to give decidable and tractable methods for the non-monotonic
aspect of reasoning. The sympathetically solitary class appears
useful for representing reasoning that is shallow in a particular
sense. Its tractability (in the non-monotonic aspect) arises from the
lack of conflict between multiple defaults, similarly to stratified
logic programs with negation by failure (there the minimization of
each predicate or ground atom corresponds to a default).

We develop the definition and results about the sympathetically
solitary class in terms of circumscription; however, they also apply
straightforwardly to Default Logic, Autoepistemic Logic, and several
other non-monotonic formalisms as well.

The sympathetically solitary class generalizes Lifschitz' solitary
class. It also includes, as a special case, the simple application of
the Closed World Assumption to unit-clausal databases, when there is
domain closure and a complete theory of equality, e.g., uniqueness of
names. However, sympathetically solitary overlaps with, and neither
includes nor is included by, the following classes: logic programs
with negation by failure; Horn; default inheritance cf. Touretzky;
predicate completion; and the general Closed World Assumption.
Last update: 1-8-98Up to Benjamin Grosof's Papers pageUp to Benjamin Grosof home page
[ IBM Research home page ]